DB
This is one I have used for a long time.
A lot of times on shared servers it already packaged with PHP. I know there is also MDB2 on the PEAR site that you can use also.
I would take the PEAR DB class and wrap it one more level if you want to maintain a constant DB connection (or at least reconnect on DB Host gone away)
Here is one I ripped from a project I did a few years back. It requires PEAR.php and Pear DB.
There is a little extra overhead in doing queries just to establish the connection. this is because I found mysql_ping unreliable at truly determining a MySQL connection resource is valid. Many time mysql_ping will return true but an actual query will result in "DB Server has gone away".